Question

The surd $\frac{12}{3+\sqrt{5}+2\sqrt{2}}$, after rationalizing the denominator becomes:

• A. $\sqrt{5}−\sqrt{2}+\sqrt{10}+1$
• B. $\sqrt{5}+\sqrt{10}+\sqrt{2}+1$
• C. $\sqrt{10}+\sqrt{2}+\sqrt{5}+1$
• D. $\sqrt{5}−\sqrt{10}−\sqrt{2}−1$

Answer 1

Answer: (B)

(i) Rationalize the denominator two times.
(ii) RF of denominator is $(3+\sqrt{5}−2\sqrt{2})$.
(iii) Rationalize the denominator twice and simplify.